Some properties of a new kind of modulus of smoothness

Vilmos Totik

doi:10.4171/zaa/98

JournalszaaVol. 3, No. 2pp. 167–178

Some properties of a new kind of modulus of smoothness

Vilmos Totik
University of Szeged, Hungary

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Abstract

The modulus of smoothness

ω (f, δ)_{φ, p} = sup_{0 < h \leq δ} ∥ Δ_{h, φ}^{2} ∥_{L^{p}}

has arisen during the investigation of positive operators of the Kantorovich type. Here we show that $ω_{φ, p}$ resembles the ordinary case $φ = 1$ and we give the characterization of those functions $f$ for which $ω (f, δ)_{φ, p} = O (δ^{2})$ . The results obtained have applications to positive operators.

Cite this article

Vilmos Totik, Some properties of a new kind of modulus of smoothness. Z. Anal. Anwend. 3 (1984), no. 2, pp. 167–178

DOI 10.4171/ZAA/98